Mass distribution | EPFL Graph Search

In physics and mechanics, mass distribution is the spatial distribution of mass within a solid body. In principle, it is relevant also for gases or liquids, but on Earth their mass distribution is almost homogeneous. Astronomy In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets. The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation. Mathematical modelling A mass distribution can be modeled as a measure. This allows point masses, line masses, surface masses, as well as masses given by a volume density function. Alternatively the latter can be generalized to a distribution. For example, a point mass is represented by a delta function defined in 3-dimensional space. A surface mass on a surface given by the equation f (x, y, z) = 0 may be represented by a density distribution g(x, y, z) δ(f (x, y, z)), where

Astrophysical applications of gravitationally lensed quasars

Alexander Eigenbrod

Gravitational lensing describes how light is deflected as it passes in the vicinity of a mass distribution. The amplitude of the deflection is proportional to the mass of the deflector, called "gravitational lens", and is generally weak, even for large masses. The faintness of this phenomenon explains why gravitational lensing remained essentially unobserved until the late 1970s (only gravitational lensing by the Sun has been observed during the solar eclipse of 1919). Before that time, gravitational lensing was considered merely as a theoretical curiosity. However, the situation dramatically changed with the discovery of the first extragalactic gravitational lens in 1979. Since then, together with the technological progress of astronomical instruments, gravitational lensing has turned from a curiosity into a powerful tool to address important astrophysical and cosmological questions. The present thesis focuses on applications related to gravitationally lensed quasars. Quasars are active galactic nuclei, where matter is heated up as it spirals down onto the central supermassive black hole. When a galaxy is located on the line of sight to a distant quasar, it acts as a gravitational lens and produces multiple images of this background source. The light of the quasar follows different paths for each of its images. Thus, variations of the intrinsic quasar luminosity are observed at different times in each image. The time delays between the images can be used to determine the Hubble constant H0, because they are inversely proportional to H0. This constant describes the current expansion rate of the Universe, and is one of the fundamental parameters of cosmological models. Many efforts have been spent over the years to determine H0, but its value is still poorly constrained. Gravitational lensing has the potential to noticeably decrease the uncertainty of H0. In practice, this requires regular and long-term monitoring of lensed quasars. We have run a series of numerical simulations to both optimize the available telescope time, and measure the time delays with an accuracy of a few percent. The results of these simulations are presented in the form of compact plots to be used to optimize the observational strategy of present and future monitoring programs. Once the time delays are measured, one can infer estimates of H0, provided several other observational constraints are available. A key element to accurately convert time delays into H0 is the redshift of the lensing galaxy. These redshift measurements are difficult because lensing galaxies are generally hidden in the glare of the much brighter quasar images. As a consequence, lens redshifts are often poorly constrained or even completely unknown. We have acquired spectroscopic data of sixteen lensing galaxies with the Very Large Telescope located in Chile. In combination with a powerful deconvolution algorithm, we determine the redshift of these sixteen lensing galaxies, which represents about 25% of all currently known quasar lensing galaxies. These results are useful for both H0 determinations and statistical studies of gravitational lenses, which can be used to provide new constraints on cosmological parameters. While the first part of this thesis focuses on the acquisition of observational constraints for the lens models, the main part consists in using the phenomenon of microlensing to determine the energy profile (or spatial structure) of quasar accretion disks. Microlensing is produced by the stars located in the lensing galaxy. These stars act as secondary lenses, and are called microlenses. Since the stars are moving in the galaxy, they induce flux and color variations in the images of the lensed quasar. These effects can be used as a natural telescope to probe the still mysterious inner structures of quasars with a spatial resolution about ten thousand times better than the capacities of current astronomical instruments, including the Very Large Telescope Interferometer. We present a three-year long spectrophotometric monitoring of the lensed quasar QSO 2237+0305, also known as the Einstein Cross, conducted at the Very Large Telescope. This monitoring reveals significant microlensing-induced variations in the spectra of the quasar images. In a subsequent analysis, we find that the source responsible for the optical and ultraviolet continuum has an energy profile well reproduced by a power-law R α λζ with ζ = 1.2 ± 0.3, where R is the size of the source emitting at wavelength λ. This agrees with the predictions of the standard thin accretion disk model and is, so far, the most accurate determination of a quasar energy profile. As a complement to our microlensing study, we have obtained high spectral and spatial resolution observations of the lensing galaxy of QSO 2237+0305. Our spectroscopic data are acquired with the SINFONI, FLAMES, and FORS2 spectrographs of the Very Large Telescope. We describe the reduction of these data, and provide the currently best and most complete determination of the kinematics of a gravitational lens. The comparison of our data with previously published dynamical models suggests that those may have overestimated the mass of the galaxy bulge. Thus, new and more sophisticated models are required. These models, combined with gravitational lensing, will provide two independent constraints on the mass distribution. This will allow to better determine the quantity and distribution of dark matter in this lensing galaxy, and especially in its extended halo.

EPFL2008

Sparse Linear Inversion for Strong Gravitational Lenses Reconstruction, Component Separation from Morphological Component Analysis with Multiple Discrimination Criteria

Rémy Elie Joseph

Strong gravitational is a natural phenomenon that produces distorted images of distant galaxies due to massive galaxies or clusters, called deflectors or lenses, lying along the line of sight. Due to the mass of the deflector, and as a result of general relativity, the light coming from galaxies at the background follows a path that appears to us as bent, thus forming magnified and sheared images. The spectacular images of gravitational lens systems give us information about a wealth of cosmological and physical processes, from the expansion of the Universe to the nature of dark matter. The study of strong gravitational lenses requires being able to extract information from images of such systems. When faced with this task, many problems arise. First, there is the problem of finding them. So far, only a few hundreds of strong gravitational lens systems are known, but future surveys are expected to bring hundreds of thousands new systems to be found amongst billions of light sources. The second problem is to be able to identify lensed features and separate them from the light profile of the foreground deflector. The third problem is to be able to reconstruct the image of a lensed background source as if it had been unaffected by lensing. The last problem is the reconstruction of the deflector's mass distribution. In practice, the last two problems have to be solved as one. Recovering the light distribution of the source requires being able to invert the distortion by the gravitational lens, which depends on its mass distribution. In turn, the lens mass distribution is constrained by the distortions applied to the source's image. In this thesis I propose to address these problems with the tools provided by sparse inverse problem solving with a particular emphasis on the problem of separating lens and source luminosity profiles. The problem of separating two overlapping light profiles is known as deblending. I introduce three new techniques for the deblending of strong gravitational lenses that exploit different properties of lens systems and that each contribute to solving the problems of strong lens finding and modelling. The first technique allows the general subtraction of galaxies light profiles in large survey in order to facilitate the search for strong gravitational lenses. The second technique allows to separate lens and source light profiles based on their difference in colour and the sparsity of a galaxy's light profile in the wavelet. This technique allows in particular to remove most of the light from foreground galaxy clusters, which facilitates the identification of lensed galaxies in view of the modelling of the cluster's mass distribution. Finally, I show that lensing itself can be used to separate the unperturbed light profile of a lens galaxy from the distorted profile of a lensed source. This technique involves the joint reconstruction of the source in its own referential based again on sparsity. At this stage, the joint reconstruction and separation is performed at fixed mass model, but this work paves the way for the development of a free form lens mass distribution reconstruction technique in the near future, based on the combination of these separation and reconstruction techniques.

EPFL2018

Improving parametric mass modelling of lensing clusters through a perturbative approach

Benjamin Emmanuel Nicolas Beauchesne, Benjamin Yvan Alexandre Clement, Jean-Paul Richard Kneib, Johan Richard

We present a new method to model the mass distribution of galaxy clusters that combines a parametric and a free-form approach to reconstruct cluster cores with strong lensing constraints. It aims at combining the advantages of both approaches, by keeping the robustness of the parametric component with an increased flexibility thanks to a free-form surface of B-spline functions. We demonstrate the capabilities of this new approach on the simulated cluster Hera, which has been used to evaluate lensing codes for the analysis of the Frontier Fields clusters. The method leads to better reproduction of the constraints, with an improvement by a factor of similar to 3-4 on the root mean square error on multiple-image positions, when compared to parametric-only approaches. The resulting models show a better accuracy in the reconstruction of the amplitude of the convergence field while conserving a high fidelity on other lensing observables already well reproduced. We make this method publicly available through its implementation in the LENSTOOL software.

OXFORD UNIV PRESS2021